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Question 1

3votes

0answers

95views

Hironaka’s polyhedron.

Hironaka proved the resolution of singularities for varieties over characteristic zero. He invented his original invariant associated to the given singular loci. I remember that after blowing ups, his ...

Pierre MATSUMI

1,061

asked23 hours ago

Question 2

0votes

0answers

54views

Intrinsic derivative

In singularity theory, one defines an intrinsic derivative for a vector bunle homomorphism $\phi: E \rightarrow F$ where $E\xrightarrow{\pi_E}B$ and $F\xrightarrow{\pi_F}B$ are vector bundles with ...

Master.AKA

1,045

askedNov 6 at 12:15

Question 3

0votes

0answers

34views

Local Milnor Number Using Gröbner Bases

In order to state my question, I will begin with some definitions.Let $\mathbb{K}$ be an algebraically closed field of characteristic zero.Suppose we have a singular irreducible plane curve defined ...

Mousa Hamieh

51

askedOct 20 at 16:24

Question 4

1vote

1answer

56views

Calculating difficulty for quotient singularities.

Let $A \colon= {\Bbb C}[X_1,\cdots,X_n]$ be a polynomial ring over ${\Bbb C}$. Let us consider the action $\sigma \colon X_i \mapsto \zeta^{e_i} X_i$ for $i = 1,\cdots,n$, where $\zeta \colon= \zeta_n$...

Pierre MATSUMI

1,061

askedOct 16 at 10:18

Question 5

0votes

0answers

33views

Statements about dimension of singularity loci in families of polynomials

I am working with some homogeneous polynomials $f\in \mathbb C[x_1, \ldots, x_n]$ belonging to families $\mathcal F$ over $\mathbb C^k$, i.e. I am considering$$f=\sum a_Ix^I, \qquad\qquad a_I\in \...

geom123

83

askedSep 23 at 8:36

Question 6

0votes

1answer

98views

Exercise 2.3.12 in Shafarevich's Basic Algebraic Geometry I [duplicate]

I am working on exercise 2.3.12 in Shafarevich's Basic Algebraic Geometry I.The problem is to classify double singular points of plain algebraic curves over an algebraically closed field $k$ of ...

Абдулкадыр Бучаев

1

askedSep 17 at 11:08

Question 7

1vote

1answer

43views

Milnor number Independent on the domain of its definition

I'm working with the Milnor number for a polynomial $f$ and am puzzled as different authors compute it in different contexts. There appears to be an implicit assumption that the Milnor number will be ...

number.seven

96

askedJul 21 at 18:52

Question 8

0votes

0answers

79views

Question about Smoothing of Vector Fields

My question concerns the smoothing of continuous vector fields V on a Riemannian manifold. Specifically, how can one approximate a continuous vector field using smooth vector fields? The approximation ...

ye cheny

21

askedJul 19 at 6:34

Question 9

0votes

1answer

51views

Codimension of singular points of hypersurface $Y\subset X$

Let $X$ be a complex manifold, and let $Y\subset X$ be an irreducible hypersurface (i.e. analytic subset of codimension 1). Lemma 2.3.22 in Huybrechts' Complex Geometry shows the sheaves $\mathcal{O}(-...

Siegmeyer of Catarina

301

askedJul 18 at 12:27

Question 10

3votes

2answers

124views

Can an immersion from the disk to a surface "double up" on its boundary?

I would like to find a simple proof or counterexample to the following claim, which has come up in some work we are doing related to curves in surfaces which bound immersed disks.Let $F$ be any ...

beanstalk

675

askedJul 1 at 17:20

Question 11

1vote

1answer

117views

Singular locus of Noetherian normal domain of Krull dimension 2

Let $R$ be a Noetherian normal domain of Krull dimension $2$. By Serre's criteria, if $\mathfrak p$ is a prime ideal such that $R_{\mathfrak p}$ is not regular, then $\mathfrak p$ must have height $2$,...

uno

1,901

askedApr 29 at 22:24

Question 12

1vote

0answers

84views

Value of algebraic generating function at $z=1$

We are given $p(z,u)$, a nonzero polynomial with real coefficients. Suppose we know that: (a) there is a generating function $g(z)$ that solves $p(z,g(z))=0$; (b) $g(z)$ has nonnegative coefficients; (...

Michele

143

askedApr 2 at 13:07

Question 13

0votes

0answers

27views

Slicing pseudomanifolds and getting sub-pseudomanifolds?

Smooth manifolds like $\mathbb{R}^n$ and $S^n$ behave nicely under slicing by coordinate hyperplanes — for example, slicing $\mathbb{R}^3$ along $x_3 = c$ yields $\mathbb{R}^2$, which is again smooth. ...

J. Zimmerman

1,199

askedMar 27 at 19:04

Question 14

0votes

1answer

52views

Is the singular support of a distribution always measure zero?

An example of a distribution whose singular support has measure zero is the delta function $δ(x)$, whose singular support is just $\{0\}$. I don't know of any examples of distributions whose singular ...

Lydia Marie Williamson

308

askedJan 15 at 22:06

Question 15

4votes

1answer

93views

Puiseux series for solution of polynomial equations

I want to study the behavior of a curve $\mathcal{C}$ implicitly defined as the zero of function $\mathbf{F}: \mathbb{R}^n\rightarrow\mathbb{R}^{(n-1)}$, $\mathcal{C}:\{\mathbf{x}\in \mathbb{R}^n \...

Franco

81

askedJan 15 at 11:35

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Stack Exchange Network

Questions tagged [singularity-theory]

Hironaka’s polyhedron.

Intrinsic derivative

Local Milnor Number Using Gröbner Bases

Calculating difficulty for quotient singularities.

Statements about dimension of singularity loci in families of polynomials

Exercise 2.3.12 in Shafarevich's Basic Algebraic Geometry I [duplicate]

Milnor number Independent on the domain of its definition

Question about Smoothing of Vector Fields

Codimension of singular points of hypersurface $Y\subset X$

Can an immersion from the disk to a surface "double up" on its boundary?

Singular locus of Noetherian normal domain of Krull dimension 2

Value of algebraic generating function at $z=1$

Slicing pseudomanifolds and getting sub-pseudomanifolds?

Is the singular support of a distribution always measure zero?

Puiseux series for solution of polynomial equations

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